(5u+8)(7-u)=0

Solution for (5u+8)(7-u)=0 equation:

(5u+8)(7-u)=0

We add all the numbers together, and all the variables

(5u+8)(-1u+7)=0

We multiply parentheses ..

(-5u^2+35u-8u+56)=0

We get rid of parentheses

-5u^2+35u-8u+56=0

We add all the numbers together, and all the variables

-5u^2+27u+56=0

a = -5; b = 27; c = +56;
Δ = b2-4ac
Δ = 272-4·(-5)·56
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-43}{2*-5}=\frac{-70}{-10}
=+7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+43}{2*-5}=\frac{16}{-10}
=-1+3/5
$